The weighted minimization criterion as a physical way to handle thickness variation in implicit structural modeling

Julien Renaudeau and Emmanuel Malvesin and Frantz Maerten and Guillaume Caumon. ( 2017 )
in: 2017 Ring Meeting, pages 1--10, ASGA

Abstract

The construction of structural geological models is commonly handled by assuming that geologi- cal features are as smooth as possible. This smoothness assumption can be related to the variational minimization of the bending energy under data constraints. Even if this assumption was proven to perform well in some geological studies, it holds major drawbacks. It approximates all layers to have a constant width on the studied domain. This is contradictory in implicit structural modeling with the observation that thickness variation in layers is a reality. In this article, the Weighted Curvature Minimization criterion is presented as a way to incor- porate thickness variation. By interpreting the concept of the bending energy in 2D, we show that penalizing this energy by an influence of proximity to data constraints is a way to solving the thickness variation issue. This criterion opens many opportunities of creating optimized implicit methods adapted to complex structural modeling. Introduction

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BibTeX Reference

@INPROCEEDINGS{Renaudeau2017,
    author = { Renaudeau, Julien and Malvesin, Emmanuel and Maerten, Frantz and Caumon, Guillaume },
     title = { The weighted minimization criterion as a physical way to handle thickness variation in implicit structural modeling },
 booktitle = { 2017 Ring Meeting },
      year = { 2017 },
     pages = { 1--10 },
 publisher = { ASGA },
  abstract = { The construction of structural geological models is commonly handled by assuming that geologi- cal features are as smooth as possible. This smoothness assumption can be related to the variational minimization of the bending energy under data constraints. Even if this assumption was proven to perform well in some geological studies, it holds major drawbacks. It approximates all layers to have a constant width on the studied domain. This is contradictory in implicit structural modeling with the observation that thickness variation in layers is a reality. In this article, the Weighted Curvature Minimization criterion is presented as a way to incor- porate thickness variation. By interpreting the concept of the bending energy in 2D, we show that penalizing this energy by an influence of proximity to data constraints is a way to solving the thickness variation issue. This criterion opens many opportunities of creating optimized implicit methods adapted to complex structural modeling. Introduction }
}